TDA vs Deferred Capital Gains

I thought the mechanics of TDA accounts is essentially the same as Deferred Capital gains taxes.

However, I saw in the curriculum different formulas for each.

FV for TDA is defined as (1+r)n*(1-Tn)

FV for Deferred Capital gains= (1+r)n*(1-Tcg) -[(1+r)n -1]*Tcg

so there’s an extra term in there. Was wondering if someone can explain why that’s there. Don’t both have taxes at end of term for gains?

The TDA formula is taxing the entire amount.

The deferred capital gains formula is taxing only the gain; i.e., there is no tax on the principal (1).

In TDA, the principal was never taxed…so when you take the money out of that account, it is taxed at that point along with interest (meaning entire amount).

However, in tax deferred gains, the principal is already after tax amount. So, only interest is taxed and hence the formula adds back the taxes on principal.

In the deferred capital gains formula, do we count the gain from the basis or the investment? Thanks

Wrong, if B=0, the basis (principal) would be also taxed what is, IMO rare situation in the real life but Tax Authority may argue that they do not recognize cost basis as tax exempt in which case whole earning amount is taxable like it was built up from zero.

Mark it, the difference between TDA and Capital gain tax

Was reviewing Example 10 from the tax reading in CFAI and was having the same question.

Within that example, 2) the taxable account with deferred capital gain had a higher FV than 3) the TDA.

So what you guys are saying is 2) is higher because 3) taxes the principal, but 2) need not be taxed again because it is already after tax to begin with?